# Spontaneous shrinkage of droplet on wetting surface in phase-field model

## TL;DR

This paper investigates the spontaneous shrinking of droplets on wetting surfaces using phase-field modeling, revealing a critical radius dependent on contact angle and other parameters, below which droplets vanish.

## Contribution

It introduces a theoretical prediction of the critical radius for droplet disappearance and verifies it through numerical simulations across various conditions.

## Key findings

- Existence of a critical radius for droplet disappearance.
- Critical radius depends on contact angle, domain size, and interface width.
- Numerical results confirm the theoretical predictions.

## Abstract

Phase field theory is widely used to model multi-phase flows. A drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy. In this paper, the spontaneous behaviour of a drop on a flat surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size and the interface width, below which the droplet will eventually disappear. In particular, the critical radius can be very large when the contact angle is hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes and the interface widths.